双螺母滚珠丝杠副导程误差与摩擦力矩关系研究

Relationship between Lead Error and Friction Torque of Double-nut Ball Screw

为了准确计算双螺母滚珠丝杠副的摩擦力矩,基于载荷和变形协调理论,分析了导程误差对载荷分布不均匀程度的影响,结合预紧力和滚珠形变提出双螺母滚珠丝杠副导程误差与摩擦力矩的关系模型。利用行程误差试验台测量不同精度等级丝杠的导程误差,并将各丝杠分别匹配同一套螺母、垫片、滚珠,组成丝杠副,测量滚珠丝杠副的摩擦力矩。结果表明,在考虑滚珠丝杠导程误差和滚珠载荷分布不均的情况下,导程误差与摩擦力矩呈线性关系,不同精度等级丝杠对应的摩擦力矩计算结果与试验值的相对误差为0~8.79%,均小于文献[6]模型的计算结果,从而验证了本文模型的有效性。

In order to calculate the friction torque of double-nut ball screw more accurately,based on the load distribution models,the influence of lead error on load distribution was analyzed.The calculation results showed that lead error directly led to uneven load distribution of ball screw and if ignoring the screw,nut elastic deformation and other errors,the axial deformation of each ball was linearly distributed.Only to calculate the axial deformation of the first ball and the lead error between balls,the total deformation of balls,preload and friction torque of ball screw can be calculated.And when the thickness of gasket was constant,the axial offset of nuts raceway curvature center and the axial offset of curvature center of screw raceway contacting the first ball to the two nuts midplane can be determined by numerical fitting of lead error and friction.Based on these,the relationship model between friction torque and lead error of double-nut ball screw was proposed.To verify the model,the lead error of screws with different accuracy levels was measured,and each screw was assembled with the same nut,gasket and balls to form a ball screw pair,and the friction torque was measured.The test results showed that the relative error between friction torque value calculated by previous model and test value was 11.75%~54.69%,while the relative error between friction torque value calculated by the model and test value was 0~8.79%.The relative error was obviously small,which indicated that the model can more accurately predict the influence of lead error on ball screw friction torque.The problem that ball screw led error and ball load distribution was not considered when calculating the friction torque of ball screw was solved,and the validity of the model was verified.